1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ghella [55]
3 years ago
11

I need help , I don’t understand this

Mathematics
1 answer:
marta [7]3 years ago
8 0
#2. First, we factor each polynomial. Then, if any terms on both the top and the bottom of the fraction match, they cancel out. So... we do just that. You end up with:

\frac{x(x-4)}{(x+9)(x-4)}

Notice there's an (x-4) on both top and bottom. So they cancel out. That leaves us with your answer of \frac{x}{(x+9)}

#3. We do the same thing as above then multiply and simplify. In the interest of space, I'll cut straight to some simplification. 

\frac{2(x+2)^{3} }{6x(x+2)} ( \frac{5}{(x-2)^{2} } )

Now we start cancelling. For the first fraction, there are 3 (x+2)'s on top and 1 on the bottom so we will cancel out the one on the bottom and leave 2 (x+2)'s on top. There are no more polynomials to cancel out so now we multiply across:

\frac{10(x+2)^{2} }{6x(x-2)^{2} }

10 and 6 share a GCF of 2 so we divide both of those by 2. This leaves us with the final answer of:

\frac{5(x+2)^{2} }{3x(x-2)^{2} }

#4. This equation introduces division and because of it, we must flip the second fraction to make the division sign into a multiplication symbol. Again for space, I'll flip the fraction and simplify in one step. 

\frac{3(x+2)(x-2)}{(x+4)(x-2)} ( \frac{x+4}{6(x+3)})

Now we do our cancelling. First fraction has (x - 2) in the top and bottom. They're gone. The first fraction has a (x + 4) on the bottom and the second fraction has one on the top. Those will also cancel. This leaves you with:

\frac{3(x+2)}{6(x+3)}

3 and 6 share a GCF of 3 so we divide both numbers by this. This leaves you with your final answer:

\frac{x+2}{2(x+3)}

#5. We are adding so we first factor both fractions and see what we need to multiply by to make the denominators the same. I'll do the former first. (10 - x) and (x - 10) are not the same so we multiply the first equation (top and bottom) by (x - 10) and the second equation by (10 - x). Because they will now have the same denominator we can combine them already. This gives us:

\frac{(3+2x)(x-10)+(13+x)(10-x)}{(10-x)(x-10)}

Now we FOIL each to expand and then simplify by combining like terms. Again for space, I'm just showing the result of this; you end up with:

\frac{x^{2}-20x+100}{(10-x)(x-10)}

Now we factor the top. This gives you 2 (x - 10)'s on top and one on bottom. So we just leave one on the top and cancel the bottom one out. This leaves you with your answer:

\frac{x+10}{10-x}

#6. Same process for this one so I won't repeat. I'll just show the work.

\frac{3}{(x-3)(x+2)} +  \frac{2}{(x-3)(x-2)} becomes

\frac{3(x-2) + 2(x+2)}{(x-3)(x+2)(x-2)} which equals

\frac{3x - 6 + 2x + 4}{(x-3)(x+2)(x-2)} giving you the final answer

\frac{5x - 2}{(x-3)(x+2)(x-2)}

#7. For this question we find the least common denominator to make the denominators match. For 5, x, and 2x, the LCD is 10x. So we multiply top and bottom of each fraction by what would make the bottom equal 10x. This rewrites the fraction as:

\frac{3x}{5} ( \frac{2x}{2x}) * ( \frac{5}{x}( \frac{10}{10}) -  \frac{5}{2x} ( \frac{5}{5}))

Simplify to get:

\frac{3x}{5}  * ( \frac{25}{10x})

After simplifying again, you end up with your final answer: 

\frac{3}{2}




You might be interested in
1/3 times what equals 1?
Mama L [17]

Answer:

3

Step-by-step explanation:

1/3 + 1/3 + 1/3 = 3/3 = 1 whole.

1/3 x 3 = 1

Hope this helps!

5 0
1 year ago
F(x) = -22 + x + 14<br> Find f(2)
Pachacha [2.7K]

Answer:

sln

f(x) =-22+x+14 put 2 in x

f(2)=-22+2+14

f(2) =38

3 0
3 years ago
A scientist is determining how fast a weed grows. Every two days the scientist measures the height of the weed. How tall will th
HACTEHA [7]

Answer:

d.

Step-by-step explanation:

8 0
3 years ago
Name all 4 angels shown in the picture
MrMuchimi
<h3>The angles are:</h3>
  1. ∠ABC
  2. ∠CBE
  3. ∠DBE
  4. ∠ABD

Hope it helps

4 0
3 years ago
Barb is making a necklace. She string 1 white bead,then 3 blue beads,then 1 white bead, and so on. Write the numbers for the fir
KiRa [710]
There will be 3 white beads out of the first 8.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Brain decided to file a claim after his car was damaged by hitting a deer.
    10·1 answer
  • What is the area of a trapezoid that has the following dimensions?
    15·2 answers
  • Christy drove 300 miles on her vacation. She drove an average of 1.25 times faster on the second 150 miles of her trip. Which ex
    5·1 answer
  • Mary went to her local zoo that Featured 8 bird exhibits.If these birds Exhibit make up 40. 0% of the zoos exhibits then how man
    6·1 answer
  • 7. A company manufactures shaving sets for $5 each and sells them for $7 each. How many shaving sets must be sold for the
    15·1 answer
  • Please help will mark brainliest
    14·1 answer
  • PLEASE HELP ME THIS IS URGENT I AM BEING TIMED!!
    13·1 answer
  • Find the base of a parallelogram with a height of 7cm and an area of 63cm
    13·1 answer
  • Pls help i don’t understand chemistry <br><br><br> Also do a step by step thing so I understand it
    13·1 answer
  • Find the area of each figure.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!